Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 11: Problem 97

A thermoelectric refrigerator removes heat from a refrigerated space at \(-5^{\circ} \mathrm{C}\) at a rate of \(130 \mathrm{W}\) and rejects it to an environment at \(20^{\circ} \mathrm{C}\). Determine the maximum coefficient of performance this thermoelectric refrigerator can have and the minimum required power input.

Short Answer

Expert verified
Answer: The maximum coefficient of performance for this thermoelectric refrigerator is 10.726, and the minimum required power input is 12.117 W.

Step by step solution

01

Convert given temperatures to Kelvin scale

To convert the given temperatures to the Kelvin scale, we simply add 273.15 to each temperature. Refrigerated space temperature (T1): \(-5^\circ\mathrm{C} + 273.15\mathrm{K} = 268.15\mathrm{K}\) Environment temperature (T2): \(20^\circ\mathrm{C} + 273.15\mathrm{K} = 293.15\mathrm{K}\)
02

Calculate the Carnot COP

The Carnot COP (COP_Carnot) for a refrigerator is defined as: COP_Carnot = \(\frac{T1}{T2 - T1}\) Substitute the values for T1 and T2 in the equation: COP_Carnot = \(\frac{268.15\mathrm{K}}{293.15\mathrm{K} - 268.15\mathrm{K}}\) COP_Carnot = \(\frac{268.15}{25} = 10.726\)
03

Determine maximum COP and minimum required power input

The maximum COP for the thermoelectric refrigerator can be obtained from the Carnot COP. Since no refrigerator can reach the efficiency of a Carnot refrigerator, the maximum COP for this thermoelectric refrigerator cannot be greater than COP_Carnot. Maximum COP (COP_max) = \(10.726\) Now, we know that the COP for a refrigerator is defined as: COP = \(\frac{\text{Rate of heat removal}}{\text{Power input}}\) With the given rate of heat removal (130 W) and the maximum COP (10.726), we can find the minimum required power input (P_min) as follows: P_min = \(\frac{\text{Rate of heat removal}}{\text{COP_max}}\) P_min = \(\frac{130\mathrm{W}}{10.726\mathrm{W}}\) P_min = 12.117455 W Minimum Required Power Input: \(12.117\mathrm{W}\) (rounded to 3 decimal places) So, the maximum coefficient of performance for this thermoelectric refrigerator is 10.726, and the minimum required power input is 12.117 W.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at \(0.20 \mathrm{MPa}\) and \(-5^{\circ} \mathrm{C}\) at a rate of \(0.07 \mathrm{kg} / \mathrm{s},\) and it leaves at \(1.2 \mathrm{MPa}\) and \(70^{\circ} \mathrm{C}\). The refrigerant is cooled in the condenser to \(44^{\circ} \mathrm{C}\) and \(1.15 \mathrm{MPa}\), and it is throttled to 0.21 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, show the cycle on a \(T\) -s diagram with respect to saturation lines, and determine ( \(a\) ) the rate of heat removal from the refrigerated space and the power input to the compressor, \((b)\) the isentropic efficiency of the compressor, and \((c)\) the \(C O P\) of the refrigerator.

Consider a two-stage cascade refrigeration system operating between the pressure limits of \(1.4 \mathrm{MPa}\) and \(160 \mathrm{kPa}\) with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where the pressure in the upper and lower cycles are 0.4 and \(0.5 \mathrm{MPa}\) respectively. In both cycles, the refrigerant is a saturated liquid at the condenser exit and a saturated vapor at the compressor inlet, and the isentropic efficiency of the compressor is 80 percent. If the mass flow rate of the refrigerant through the lower cycle is \(0.11 \mathrm{kg} / \mathrm{s}\), determine ( \(a\) ) the mass flow rate of the refrigerant through the upper cycle, \((b)\) the rate of heat removal from the refrigerated space, and ( \(c\) ) the COP of this refrigerator.

A refrigerator operates on the ideal vapor-compression refrigeration cycle and uses refrigerant-134a as the working fluid. The condenser operates at 300 psia and the evaporator at \(20^{\circ} \mathrm{F}\). If an adiabatic, reversible expansion device were available and used to expand the liquid leaving the condenser, how much would the COP improve by using this device instead of the throttle device?

Using EES (or other) software, investigate the effect of the condenser pressure on the COP of an ideal vapor-compression refrigeration cycle with \(\mathrm{R}-134 \mathrm{a}\) as the working fluid. Assume the evaporator pressure is kept constant at \(150 \mathrm{kPa}\) while the condenser pressure is varied from 400 to \(1400 \mathrm{kPa}\). Plot the COP of the refrigeration cycle against the condenser pressure, and discuss the results.

A gas refrigeration system using air as the working fluid has a pressure ratio of \(5 .\) Air enters the compressor at \(0^{\circ} \mathrm{C} .\) The high- pressure air is cooled to \(35^{\circ} \mathrm{C}\) by rejecting heat to the surroundings. The refrigerant leaves the turbine at \(-80^{\circ} \mathrm{C}\) and enters the refrigerated space where it absorbs heat before entering the regenerator. The mass flow rate of air is \(0.4 \mathrm{kg} / \mathrm{s}\). Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using variable specific heats, determine ( \(a\) ) the effectiveness of the regenerator, \((b)\) the rate of heat removal from the refrigerated space, and \((c)\) the \(\mathrm{COP}\) of the cycle. Also, determine \((d)\) the refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies.
See all solutions

Recommended explanations on Physics Textbooks

Electricity

Read Explanation

Waves Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Astrophysics

Read Explanation

Wave Optics

Read Explanation

Particle Model of Matter

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free